International Journal For Multidisciplinary Research

E-ISSN: 2582-2160   •   Impact Factor: 9.24

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Some Unique Fixed-point Theory in Different Spaces

Author(s) AKANKSHA SINGH, Dr. MANISH KUMAR SINGH, Dr. RITA SHUKLA
Country India
Abstract A variety of subfields within mathematics, such as optimisation, nonlinear analysis, and dynamical systems, are significantly dependent on the concept of fixed points. The term "fixed point of the function" refers to the point that is mapped to itself while a function is being mapped. The fact that fixed points in different types of spaces are distinct from one another has a substantial impact on the stability and behaviour of these systems. This abstract presents a discussion of new insights into the concept of unique fixed points in a variety of mathematical spaces, such as metric spaces, Banach spaces, and topological spaces, among others. According to the Banach Fixed-Point Theorem, which is often commonly referred to as the Contraction Mapping Theorem, contractive mappings in metric spaces are guaranteed to have fixed points that are both unique and already present. It is possible to generalise this classical conclusion to a number of non-Archimedean spaces including fuzzy metric spaces, which sheds insight on the dynamics of fixed points under weaker dynamics. In these spaces, the singularity of fixed points is often brought about by higher contraction characteristics or additional limits on the mappings.
Keywords Fixed-Point Theorem, Metric Spaces, Banach Contraction Principle, Banach Spaces.
Published In Volume 7, Issue 5, September-October 2025
Published On 2025-10-16
DOI https://doi.org/10.36948/ijfmr.2025.v07i05.57981
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E-ISSN 2582-2160
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